Daily Practice · Higher Plus
August 2008 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2008, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2008 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2008
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2008y is inversely proportional to x^2. When x = 3, y = 36. Work out y when x = 6.
- 2nd August 2008In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 3rd August 2008The probability of winning a game is 7/10. A player expects 84 wins. How many games did they play?
- 4th August 2008On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 5th August 2008Expand and simplify (4 + sqrt(10))(4 - sqrt(10)).
- 6th August 2008Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 7th August 2008y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 8th August 2008In a vector proof you find that vector PQ = 6a + 2b and vector RS = 30a + 10b. What does this show about PQ and RS?
- 9th August 2008A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 10th August 2008A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 1.4. How many values in total?
- 11th August 2008A block has mass 270 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th August 2008f(x) = 5x + 4 and g(x) = 5x - 8. Work out fg(2).
- 13th August 2008y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 9.
- 14th August 2008A cuboid measures 3 cm by 6 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th August 2008A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th August 2008On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th August 2008x = 181 and y = 33, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th August 2008The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 19th August 2008A train slows steadily from 14 m/s to rest in 4 seconds. Work out its deceleration.
- 20th August 2008A cuboid measures 7 cm by 8 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st August 2008A bag holds 3 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd August 2008A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 23rd August 2008A car covers 590 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 24th August 2008A quadratic sequence starts 4, 15, 30, 49. Work out the second difference, and the coefficient of n^2.
- 25th August 2008y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 26th August 2008The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 27th August 2008A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 28th August 2008On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 29th August 2008Rationalise the denominator of 6/sqrt(2), giving your answer in its simplest form.
- 30th August 2008Solve x^2 + 3x - 10 > 0.
- 31st August 2008y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.